We assess the possibility of detecting and characterizing the physical state of the missing baryons at low redshift by analyzing the X-ray absorption spectra of the gamma-ray burst (GRB) afterglows, measured by a microcalorimeter-based detector with 3 eV resolution and 1000 cm2 effective area and capable of fast repointing, similar to that on board of the recently proposed X-ray satellites EDGE and XENIA. For this purpose we have analyzed mock absorption spectra extracted from different hydrodynamical simulations used to model the properties of the warm hot intergalactic medium (WHIM). These models predict the correct abundance of O VI absorption lines observed in UV and satisfy current X-ray constraints. According to these models space missions such as EDGE and XENIA should be able to detect ~60 WHIM absorbers per year through the O VII line. About 45% of these have at least two more detectable lines in addition to O VII that can be used to determine the density and the temperature of the gas. Systematic errors in the estimates of the gas density and temperature can be corrected for in a robust, largely model-independent fashion. The analysis of the GRB absorption spectra collected in three years would also allow to measure the cosmic mass density of the WHIM with ~15% accuracy, although this estimate depends on the WHIM model. Our results suggest that GRBs represent a valid, if not preferable, alternative to active galactic nuclei to study the WHIM in absorption. The analysis of the absorption spectra nicely complements the study of the WHIM in emission that the spectrometer proposed for EDGE and XENIA would be able to carry out thanks to its high sensitivity and large field of view
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